The present invention generally relates to piezoelectric devices and more particularly to a piezoelectric transformer supplied with an input a.c. current for stepping up or stepping down a voltage thereof.
Conventionally, stepping up or stepping down of a.c. voltage has been achieved by electromagnetic transformers. The electromagnetic transformer generally has a primary side winding and a secondary side winding coupled electromagnetically by a magnetic core. In such a construction, it is generally inevitable that the transformer has a substantial size. On the other hand, there are applications, particularly for the information processing apparatuses including the CRT displays, electrostatic printers, DC converters, and the like, wherein a reduced size is demanded for the transformer. Further, some of the applications require a high output voltage such as several thousand volts in addition to the reduced size, while there are applications where a large output current is needed as in the case of the power transformers.
Meanwhile, there is a proposal to use piezoelectric crystals or ceramics for the transformer (C. A. Rosen, Proc. Electronic Components Symp. p. 205, 1957). There, primary side and secondary side electrodes are provided on a piezoelectric substrate, and a piezoelectric vibration is induced in the piezoelectric substrate in response to an application of a primary size voltage across the primary side electrodes. The piezoelectric vibration thus induced is converted to a voltage at the secondary side electrodes.
FIGS. 1(A) and 1(B) show the conventional piezoelectric transformer proposed in the above reference.
Referring to the drawings, the piezoelectric transformer includes a piezoelectric substrate 2 that in turn is formed substantially from two portions, one having a polarization P.sub.i that acts in the direction of the thickness of the substrate and the other having a polarization P.sub.o that acts in the longitudinal direction of the substrate 2. In correspondence to the first portion of the substrate 2, a pair of primary side electrodes 4a and 4b are provided to oppose with each other, and a primary side voltage V.sub.i is applied across the electrodes 4a and 4b. Thereby, a vibration is induced in the substrate 2 in the vertical direction as shown by the lines d and d', wherein the lines d and d' represent the distribution profile of the displacement that is caused in the substrate as a result of the vibration at two different instances. Further, at the longitudinal end of the substrate 2, there is provided a secondary side electrode 6 for converting the piezoelectric vibration to an electric voltage V.sub.o. There, the electrode 4b at the bottom of the substrate 2 is used also for one of the secondary side electrode, and the output voltage V.sub.o is obtained across the electrode 6 and the electrode 4b. In correspondence to the node of vibration, there is provided a mechanical support 8 for supporting the substrate 2 such that the substrate 2 vibrates freely.
The step-up or step-down operation of the piezoelectric transformer is represented as EQU V.sub.o /V.sub.i .infin.K.sub.31.K.sub.33.Q.sub.1.L.sub.2 /L.sub.1 ( 1)
wherein K.sub.31 represents the electromechanical coupling coefficient for the transverse effect while K.sub.33 represents the electromechanical coupling coefficient for the longitudinal effect. Further, L.sub.1 stands for the thickness of the substrate 2, and L.sub.2 represents the longitudinal length of the second portion of the substrate 2. See FIG. 1(B). Further, Q.sub.1 represents the quality factor or Q of the substrate 2. From this equation, it will be understood that one can control the step-up or step-down ratio as desired by setting the geometrical parameters L.sub.1 and L.sub.2 as well as by suitably choosing the material parameters K.sub.31, K.sub.33 and Q.sub.1.
In this conventional device, however, there arises a problem in that the preparation of the substrate 2 that has two portions with respective, mutually different polarizations, is difficult. For example, the substrate 2 may be formed by joining a first piezoelectric plate having the polarization P.sub.i and a second piezoelectric plate having the polarization P.sub.o with each other by an adhesive. However, the application of the voltage to the primary side electrodes 4a and 4b induces a large amplitude vibration particularly at the part where the first plate and the second plate are joined with each other, and there arises a problem that the piezoelectric substrate may be damaged or destroyed during the use of the device. Further, the piezoelectric transformer of this prior art has a large internal resistance due to the large distance between the electrode 4b and the electrode 6. Because of this, the piezoelectric transformer of this proposal is not suitable for power transformers or DC-DC converters where a large output current is required.
In order to eliminate these problems and to provide a piezoelectric transformer that endures for the practical use, the inventors of the present invention have proposed in the Japanese Patent Application 2-249574 filed Sep. 18, 1990 and in the corresponding United States patent application Ser. No. 761,049, a piezoelectric transformer that uses a longitudinal mode vibration or longitudinal wave excited in a piezoelectric substrate by the piezoelectric transverse effect.
Referring to FIGS. 2(A) and 2(B) showing this conventional device, the piezoelectric transformer uses a piezoelectric substrate 12 of 140.degree. rotated Y-cut LiNbO.sub.3 having a polarization P in the Z-direction. The substrate 12 is cut from a single crystal ingot of LiNbO.sub.3 having the X-axis, Y-axis and Z-axis in correspondence to the crystal anisotropy, with an orientation such that a longitudinal direction of the substrate 12 defined as the Z'-direction is rotated about the X-axis an angle of 140.degree.. See the crystal orientation shown in FIG. 3. Thereby, the Y'-direction that extends in the vertical direction to the substrate 12 also forms the angle of 140.degree. with respect to the original Y-axis. On the other hand, the transverse direction defined as the X'-direction of the substrate 12 coincides with the X-axis. It should be noted that the foregoing orientation is chosen to obtain a maximum electromechanical coupling k.sub.33.
On the upper and lower major surfaces of the substrate 12, primary side electrodes or input electrodes 14a and 14b are provided to oppose with each other across the substrate 12 at a first half of the substrate 12. Further, secondary side electrodes or output electrodes 16a and 16b are provided to oppose with each other across the substrate 12 at a second half of the substrate 12. See the perspective diagram of FIG. 2(A). There, the electrodes 14a and 16a are aligned in the longitudinal direction on the upper major surface of the substrate 12, while the electrodes 14b and 16b are aligned also in the longitudinal direction at the lower major surface of the substrate 12. In the this conventional device, the longitudinal size and hence the area of the electrode 14a are set substantially equal to those of the electrode 16a. Similarly, the longitudinal size and hence the area of the electrode 14b are set substantially equal to those of the electrode 16b.
In operation, a longitudinal wave is excited in the substrate 12 upon the application of the input a.c. voltage V.sub.i across the electrodes 14a and 14b. Thereby, the longitudinal wave propagates in the longitudinal direction of the substrate in correspondence to the piezoelectric lateral effect and establishes a resonance with the frequency that is determined by the longitudinal size of the substrate. For example, the longitudinal size of the substrate 2 may be set equal to about one-half of the wavelength of the longitudinal wave excited in the substrate 12. The resonant vibration thus formed in the substrate 12 is then converted to an electric output V.sub.o at the electrodes 16a and 16b. As the direction of polarization is uniform in the substrate 12, the localized concentration of stress that may damage or destroy the substrate as in the case of the device of FIGS. 1(A) and 1(B) does not occur.
The step-up ratio V.sub.o /V.sub.i is given as EQU V.sub.o /V.sub.i .infin.k.sub.i.k.sub.o.Q.sub.a.l.sub.01 /l.sub.02 ( 2)
where k.sub.i and k.sub.o represent respectively the electromechanical coupling coefficient at the part where the input electrodes 14a and 14b are provided and the electromechanical coupling coefficient at the part where the output electrodes 16a and 16b are provided. Further, Q.sub.a represents the quality factor of the substrate 12, l.sub.01 represents the distance between the electrodes 14a and 14b, and l.sub.02 represents the distance between the electrodes 16a and 16b. In the prior art device in consideration, the ratio l.sub.01 /l.sub.02 becomes to about 1.
FIG. 4 and FIGS. 5(A)-5(C) show the operational characteristics of the piezoelectric transformer of the foregoing prior art based upon the well known Mason's equivalent circuit model, wherein FIG. 4 shows the change of input impedance with the frequency of the input a.c. voltage V.sub.i.
Referring to FIG. 4, the input impedance Z is inductive at the lower frequency range while changes drastically to capacitive at a resonant frequency f.sub.r as demonstrated by the phase angle term of Z that changes from -90.degree. to +90 .degree.. Hereinafter, the resonant frequency f.sub.r will be defined as the frequency at which the phase angle assumes the value of -90.degree..
In this conventional piezoelectric transformer, the resonant frequency f.sub.r changes in response to the load that is connected across the electrodes 16a and 16b as shown in FIG. 5(A).
Referring to FIG. 5(A), the resonant frequency f.sub.r changes stepwise with load resistance R.sub.1 at the value of about 10.sup.4 .OMEGA., and in correspondence to this stepwise change of the resonant frequency f.sub.r, there appears a peak in the input resistance R.sub.r that is the input resistance in the state where the resonance explained with reference to FIG. 4 is established. See FIG. 5(B). More specifically, the input resistance R.sub.r increases with the load resistance R.sub.1 in the range where the value of the load R.sub.1 is smaller than about 10.sup.4 .OMEGA., and can reach as high as 10.sup.4 .OMEGA. or more.
Most importantly, the step-up ratio V.sub.o /V.sub.i becomes unity when the load resistance R.sub.1 connected across the output electrodes 16a and 16b is smaller than about 10.sup.4 .OMEGA.. See FIG. 5(C). This means that no stepping-up or stepping-down is obtained in the piezoelectric transformer when the load R.sub.1 connected to the transformer has a resistance of smaller than 10.sup.4 .OMEGA.. In other words, the piezoelectric transformer of this prior art does not function as the step-up or step-down transformer when used as a power transformer that produces a large output current.
Further, when using the piezoelectric transformer for various applications, there has been a problem in that the output waveform of the piezoelectric transformer is distorted significantly due to the unwanted resonance occurring at various frequencies. It is thought that such unwanted resonance occurs by the mechanical resonance of the piezoelectric substrate at a number of vibration modes, and there is a demand for a piezoelectric transformer in which the distortion is minimized from the output voltage.